Scott Boras’s Tall Tale

With Albert Pujols off the free agent board, Prince Fielder finds himself next in line to an immense pay day. Although Fielder hasn’t put up quite the numbers Pujols has, his accomplishments to date, at age 27, are nothing short of spectacular. He is the type of player that can immediately impact a line-up in a profound way, but questions of how he’ll age, remain. The main issue with Fielder is his weight, but this past week super-agent Scott Boras brought up a new component of Fielder’s body-type;

“Everyone talks to me about Prince’s body, but when you have that 5’11” strike zone, that is a huge advantage and that’s why that on-base percentage is sitting there. Those pitchers have to put the ball into a smaller window and I believe that it’s more difficult to do.” – Scott Boras

On the surface, this argument makes sense. Smaller players have smaller strike zones, so it follows that smaller strike zones would imply more balls, more walks, and higher on base percentage. At 5-11, Fielder is not short (I would kill to be 5-11), but he is below league average. The average height in my dataset (2006-2011 players with at least 400 Pas) is 6’1”. My first step was to plot height against BB%. I think it is fair to assume that the OBP advantage that a short player may have would be derived from walks.

While the model doesn’t tightly fit the data (R^2=5.5%), the slope is not trivial and is significantly upward sloping. Part of the low R^2 can be attributed to fact that height is measured in inches and not something more granular. Additionally, it is worth noting that is my experience, the height measurements are not the most reliable. It is clear from the plot above, and the regression analysis, that Boras is incorrect. Shorter players do not have higher BB%, in fact, they have lower BB%. Part of the problem with this simplistic analysis is there may be a lurking variable at play, namely weight. There is a strong correlation between weight and height, and what we may be seeing in the plot above is the correlation between weight and BB%. This makes more sense, because heavier players are on average stronger and thus more powerful, and we know that more power means more BBs.
If we instead plot BB% against weight we get a similar graph:

Again, the slope is significantly positive, and this fit is better, and the p-value of the slope is lower (meaning more significant).
The next step is to control for weight. We can do this by first regressing BB% on Weight, and looking at the residuals (BB%-Res). BB%-Res is the component of BB% that is not explained by Weight. Next we regress Height on Weight and take the residuals Ht-Res. Ht-Res is the component of Height not explained by Weight. Finally, we regress BB%-Res on Ht-Res. In doing this, Weight is no longer a lurking variable.

Here we see that there is a statistically significant positive relationship between BB% and height when controlling for weight.

It is now clear, that Mr. Boras is not only incorrect in asserting that shorter players have an obp% advantage due to their height, but even after controlling for weight, the exact opposite relationship exists. This should not discount Fielder’s value, but I think we can throw away the notion that shorter players have higher BB% (or OBP), because of a smaller strike zone. It is unclear why taller players have an advantage (small, but statistically significant), and I would be interested to hear your theories.